Is it possible to create an own object data type through Python?
One can extend the objects in Blender (if you want to make your own).
For example take a look at BoltFactory, IvyGen etc, many addons add objects.
However keep in mind that Blender Python is implemented as an API
Adding stuff by inheriting from a base class is possible in python however the rest of the program will not know it, ea dont suspect that cycles or eevee or fluidsims or particles will understand your custom object attributes /methods.

If its only about adding some extra valeu property (maybe fro some other script) then in the normal view of object properties you can add custom attributes as well, perhaps thats usefull to you. 
(object tab => add custom properties)

You might not even require python to do so, but if you want to that in code:

bpy.ops.wm.properties_edit(data_path="object", property="demo", value="1.0", min=0, max=1, use_soft_limits=False, soft_min=0, soft_max=1, description="this is demo tool tip")